Multidimensional quasiperiodic antiphase dynamics.

We study analytically the (N-1)-fold degenerate Hopf bifurcation at which N stationary modes with identical parameters become unstable in a model of a solid-state laser with intracavity second harmonic generation. We use the normal form method and exploit the symmetries of the problem. Up to N=3, stable periodic antiphased solutions emerge from the Hopf bifurcation. For N=4, stable quasiperiodic solutions arise from the degenerate Hopf bifurcation. For N>4, the quasiperiodic solutions may be unstable. Then chaotic itineracy is observed numerically close to the degenerate Hopf bifurcation.